SOLUTION: A group of boys desiring to group a team to buy a ball. If there had been 3 boys fewer, each would have paid one dollar more; and if there had been 4 boys more, each would have pai
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Question 1182223: A group of boys desiring to group a team to buy a ball. If there had been 3 boys fewer, each would have paid one dollar more; and if there had been 4 boys more, each would have paid 75 cents less. Find the cost of the ball.
->Please help me how to solve this problem step by step.. Thanks in advance!!
Found 2 solutions by greenestamps, mananth:
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!
Let x be the cost of the ball
Let y be the number of boys
x/y = cost per boy
x/(y-3) = cost per boy if there had been 3 fewer boys
x/(y+4) = cost per boy if there had been 4 more boys
If there had been 3 boys fewer, each would have paid one dollar more...:
[1]
... and if there had been 4 boys more, each would have paid 75 cents less:
[2]
Solve each equation by multiplying through by the least common denominator.
[1]
[3]
[2]
[4]
Eliminate x between [3] and [4] by multiplying [3] by 16 and [4] by -3 and adding:
y=0 or y=12. Clearly y=0 makes no sense in the problem, so y=12.
So the number boys is y=12.
Use y=12 in either [1] or [2] to find the cost of the ball.
I leave that much to you....
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let each boy pay x
and number of boys be y
there had been 3 boys fewer, each would have paid one dollar more
(y-3)(x+1) = xy
xy+y-3x -3 =xy
y-3x=3
y=3x+3----------------(1)
(y+4)(x-3/4) = xy
xy -(3/4)y +4x -3 =xy
-3/4 y +4x = 3
multiply by 4
-3y +16x =12--------------(2)
substitute y in (2)
-3(3x+3)+16x =12
-9x-9 +16x =12
7x =21
x= 3
y=3x+3
y= 3*3 +3
y=12
Cost of Ball = 4*12 =48
$48
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